On the Lie structure of zero row sum and related matrices

Abstract

AbstractWe study the structure of zero row sum matrices as an algebra and as a Lie algebra in the context of groups preserving a given projection in the algebra of matrices. We find the structure of the Lie algebra of the group that fixes a given projection. Details for the zero row sum matrices are presented. In particular, we find the Levi decomposition and give an explicit unitary equivalence with the affine Lie algebra. An orthonormal basis for zero row sum matrices appears naturally.